Nice one.
I should have said by putting the rails and boards with the flat/ finished side facing out you get easy access to as much of your land as possible. Although you have not.lost any land if you fence it inside the boundary you make it difficult to access and there are/used to be legal...
Ah but you lost a small part of your land that way. OK if its a big garden but on a small terrace in town in I'd always want to keep all my land.
Going back to the OP. If the neighbour doesn't accept its her fence basd on posts and rails I'd keep the post holes in the same place but reverse...
Does the fence have posts? These will be set at the boundary line, and the rails set so that the fence boards/panels are also right on the boundary.
Posts are usually wider than the fence panels so the flat (neat) side of the fence faces outwards to face your neighbour. Your side will have...